Queen's Club champion Roddick, who had never gone further the third round in his two previous visits here, fired nine aces to subdue the challenge of a dogged Robredo.
The fast-serving American, 20, had won all four of his previous four meetings against the 25th seed, but there was little to separate the pair in the opening set.
Both failed to convert their only break point opportunities early on and instead traded blistering blows from the baseline as the set headed for a tiebreak.
Roddick started off the tiebreak with a 131 mph (210.8 kph) ace before clinching it 7-5 when Robredo slapped a forehand into the net.
Having secured the first break of the encounter at 4-3 in the second, Roddick cranked up the power to run away with the match in one hour 54 minutes.
NADAL'S RUN ENDED BY PARADORN
Rafael Nadal-Parera's bold bid to become the youngest player since Bjorn Borg to reach the fourth round of the men's singles at Wimbledon ended on Friday when he was beaten 6-4, 6-4, 6-2 by Thai Paradorn Srichaphan.
The Spaniard, who turned 17 earlier this month, eventually succumbed but not before providing the enthralled court one crowd with a tantalising glimpse of the future.
After an error-strewn opening set, Nadal appeared to have gained the upper hand in the second when he broke to lead 4-2. But, for once looking like a raw teenager, he threw away his advantage and was swiftly punished.
Battle-hardened 12th seed Paradorn, looking increasingly dangerous after scrambling through the first two rounds in five sets, broke twice in a row to gain a two-set lead and romped through the third with some trademark forehand bombs.
Paradorn, who is in the fourth round of a Grand Slam for the first time, faces a mouthwatering clash with bookmakers' favourite Andy Roddick for a place in the quarter-finals.
